There is a tool to get infobox data from Wikipedia into Wikidata: https://pltools.toolforge.org/harvesttemplates/

The easily parsable Infobox data can probably already be found in Wikidata (assuming there is a property).

So am I right in thinking Wikidata is sort of scraped from Wikipedia internally?

The other way round seems better, but obviously too late.

A lot of items don't have a wikipedia page, but all wikipedia, wikitravel, wiki* pages have a wikidata item (see "Wikidata item" link of the left side of the pages).

Some wikipedia infoxes are based on wikidata. I can't find an example, but here some links:

* https://commons.wikimedia.org/wiki/Commons:Wikidata_infobox_...

* https://commons.wikimedia.org/wiki/Template:Wikidata_Infobox

* https://en.wikipedia.org/wiki/Template:Infobox_person/Wikida...

There are lexeme too, and it is not based on wiktionary. Search the prefix "L:" (without quote).

Example:

* https://www.wikidata.org/w/index.php?search=L%3Acat&search=L...

* https://www.wikidata.org/wiki/Lexeme:L7

Also, there are a lot of tools on toolforge.org. One is reasonator which produce sentences from a wikidata item: https://reasonator.toolforge.org/?q=Q1339